no one has even mentioned Orange, in fact, that's what Jimmy page used on 'since I've been lovin you' by Led Zep. There's an orange head with three channels.
no one has mentioned Soldano, they do some outstanding head amps! one of the best, check out their three channel amps.
Mesa Boogie Dual rectifier, has 3 channels and it can do what you described but not fully.
If I was you I'd contact Custom Audio amplifiers, made by John Shur, as they're that good I recon it's actually possible with one to get the tone youre after. It certanly isn't impossible, but you're looking at £3,500 + just for the head. To me Custom Audio are the best of the best, I mean Warren Cuccurullo used them in the 90s! to give you an idea of the tone of a Custom Audio amp, just listen to the album 'Thanks to Frank' from the 90s. Now that's what I call a real $%ing amp! he used the CA100 head, which is now a classic.